Can feature engineering change the selection of the model according to the minimum description length?
I think the wrong assumption here is that you've forgotten the cost of encoding the new features!

MDL should be considered relative to the original or raw dataset. The idea is that you want to find an expression you could send to someone else that encodes the structure of the dataset in terms of the original variables. If you define new features, you need to send a description of those features along with your model. 

To make this clearer, imagine you call me up on the phone, and we're both looking at your left hand image. You say to me 'Yeah, you just draw a line through it at $p=a$'. The natural question for me to ask is 'What's p?'. If you have to tell me what $p$ is, then it's part of the description length. 

A circular model for your lefthand image does have a MDL for its decision boundary of something like $(x−a)^2+(y−b)^2=c$. However, the feature transformation you've selected has a description length of $p=(x-a)^2 + (y-b)^2$. It should be clear that the description lengths for the linear model through $p$ and the circular model through $x$ and $y$ are identical.